Topology optimization of continuum structures is a relatively new branch of the
structural optimization field. Since the basic principles were first proposed by
Bendsøe and Kikuchi in 1988, most of the work has been devoted to the so-called
maximum stiffness (or minimum compliance) formulations. However, for the past
few years a growing effort is being invested in the possibility of stating and solving
these kinds of problems in terms of minimum weight with stress (and/or displacement)
constraints formulations because some major drawbacks of the maximum
stiffness statements can be avoided.
Unfortunately, this also gives rise to more complex mathematical programming
problems, since a large number of highly non-linear (local) constraints at the element
level must be taken into account. In an attempt to reduce the computational
requirements of these problems, the use of a single so-called global constraint has
been proposed. In this paper,we create a suitable class of global type constraints by
grouping the elements into blocks. Then, the local constraints corresponding to all
the elements within each block are combined to produce a single aggregated constraint
that limits the maximum stress within all the elements in the block. Thus,
the number of constraints can be drastically reduced. Finally, we compare the results
obtained by our block aggregation technique with the usual global constraint
formulation in several application examples.
1 Introduction
Topology optimization problems have been usually stated as maximum stiffness
(minimum compliance) continuum formulations. However, different approaches